Question

A capillary of the shape as shown is dipped in a liquid. Contact angle betweeen the liquid and the capillary is and effect of liquid inside the meniscus is to be neglected. $T$ is surface tension of the liquid. $r$ is radius of the meniscus, $g$ is acceleration due to gravity and p is density of the liquid then height $h$ is

• A. greater than $\frac{2T}{\text{rpg}}$
• B. Equal to $\frac{2T}{\text{rpg}}$
• C. Less than $\frac{2T}{\text{rpg}}$
• D. of any value depending upon actual values

Answer 1

The correct option is C Less than $\frac{2T}{\text{rpg}}$

the weight of the liquid in the capillary is balanced by the surface tension, given by,

$T\times 2\pi r=\pi r^2{h}_1\rho g$

$h_1=\frac{2T}{r\rho g}$

from the figure, the weight of the liquid is more in the tapered table than the radius of the capillary, in order to balance that, we have,

$h<h_1$

$\therefore h<\frac{2T}{r\rho g}$